Firefighting personnel need to know when the environment they are operating in is too hot for their personal protective equipment (PPE). Often, it is the face piece of the Self Contained Breathing Apparatus (SCBA) that is the first component to fail in a high temperature environment, which can lead to catastrophic accidents (FIG. 1).
Mensch et al. 2011, Donnelly et al. 2006 have classified fires based on the surrounding air temperature and radiative heat flux to which the firefighter is exposed (FIG. 2). Class I fires have air temperatures of 10-100° C. (50-212° F.) with heat fluxes of 0.1-1 kW/m2 (whichever comes first). Class I fires are routinely encountered and one can work for about 25 min under these conditions while wearing ordinary PPE (turnout gear and SCBA). Class II fires are more serious with air temperatures of 100-160° C. (212-320° F.) and/or heat fluxes of 1.0-2.0 kW/m2, and while routinely encountered, exposure is limited to about 15 min. Class III fires are dangerous and less than 5 min should be spent in a Class III fire; temperatures are on the order of 160-260° C. (320-500° F.) with heat fluxes of 2.0-10.0 kW/m2. Class IV fires are extremely dangerous and represent conditions that can be lethal. The temperatures that accompany Class IV fires are at least 260° C. (500° F.) and can be as high as 1000° C. (1832° F.) if a flash over occurs. Heat fluxes of at least 10 kW/m2 are present, and have been measured to be as high as 100 kW/m2 during a flashover. Because flashovers are practically impossible to predict with any significant lead time, immediate withdrawal is required when Class IV conditions are detected. Under Class IV conditions, the firefighter's PPE will rapidly fail, in particular the faceplate of the SCBA, which is made from high-temperature polycarbonate that has a maximum operating temperature of about 200° C.
A general problem is that modern PPE is so effective at protecting firefighters that it is difficult for them to know if the external environment has become dangerous until it may be too late. To address this issue a Personal Alert Safety System (PASS) devices can incorporate temperature detectors. Unfortunately, the response time of these devices is too slow to be useful (in some cases tens of minutes) since temperatures and radiant heat fluxes can change in a matter of seconds.
Heat is transferred to the firefighter (and his/her PPE) by three different mechanisms: convection, radiation and conduction. Convective heat transfer is important because it can cause failure in the firefighter's PPE. In the context of firefighting, convection transfers energy by contact of heated air with the PPE that is at a lower temperature. The general expression for the net heat flux (Btu/ft2/hr) is given by Equation 1, where hconv is the convective heat transfer coefficient, a proportionality constant, that has a value that depends on the geometry of the object being heated (or cooled), its orientation relative to the direction of air flow, and the velocity of the air. Either direct measurement or semi-empirical correlations can used to determine the value of hconv. In free convection, fluid flow causes heat transfer as a result of buoyancy differences in the fluid adjacent to the object when there is a difference between the object's surface temperature and the temperature of the fluid. Since the fluid velocity is relatively low, free convection heat transfer coefficients tend to be low (e.g. h˜5-50 W/m2K). In forced convection, the fluid flows much faster and the heat transfer coefficients can be much larger (e.g. 50-2500 w/m2K).
Equation 1. Heat flux by convection:q/A=hconvΔT=hconv(T2−T1)
The most dangerous source of heat in a fire is infrared (IR) radiation and the greatest amount of its energy comes from flame emission. Since IR is electromagnetic radiation and travels at the speed of light, changes in IR emission are felt as quickly as the source temperature changes. The wavelengths which carry the most energy at fire temperatures are between λ=0.25 μm and λ=6 μm. The energy of electromagnetic (EM) radiation Eλ, in terms of wavelength is given by Equation 2, where h is Planck's constant (6.62×10−34 m2 kg/s), λ is the wavelength in meters, and c is the speed of light in vacuum (3×108 m/s). With these units Eλ is in Joules.
Equation 2. EM energy as a function of wavelength:
      E    λ    =                    h        Plank            ⁢      C        λ  
The wavelength corresponding to the highest energy emitted by a hot object depends on its temperature and obeys Plank's radiation law (FIG. 3), which is described by Equation 3, where kB is Boltzmann's constant (kB=1.380×10−23 m2 kg/s2/K) (Bird et al. 1960). While this equation applies only for a perfect radiator (i.e. a blackbody) it illustrates why wavelengths between 0.25 μm and 6 μm are the most dangerous for firefighters; S(λ) is at its maximum at these wavelengths at typical fire temperatures (FIG. 4).
Equation 3. Planck's law for intensity [S(λ)] as a function of source temperature (T)
      S    ⁡          (      λ      )        =                    2        ⁢        π        ⁢                                  ⁢                  c          2                ⁢        h                    λ        5              ⁢          1                        e                      hc                          λ              ⁢                                                          ⁢                              k                B                            ⁢              T                                      -        1            
Unlike convection and conduction where the driving force for heat transfer is the linear difference between the hot and cold temperatures (i.e. ΔT=Thot−Tcold), the driving force for radiative heat transfer is (Th4−Tc4), which makes small increases in the source temperature (Th) have a large effect on the amount of energy radiated. The net radiative heat flux is given by
Equation 4, where F is the view (configuration) factor, σ is the Stefan-Boltzmann constant (σ=5.67×10−8 W/m2/K4) and ε is the emissivity.
Equation 4. Thermal radiation heat flux.q/A=hconvΔT=hconv(T2−T1)
Emissivity (ε) is one an important quantity in radiation heat transfer because it determines how efficiently radiant energy is absorbed. For objects that differ from a blackbody only in the percentage of radiation absorbed or emitted an each wavelength are called graybodies and have emissivities of ε<1. The emissivities listed in various tables for different materials are usually hemispherical emissivities which represent the average emissivity over all wavelengths at all angles from a surface and require that none of the radiation be reflected (i.e. no shiny surfaces).
A true blackbody is a theoretical object that is a perfect absorber and emitter of electromagnetic radiation at all wavelengths and is described by Equation 3. Real surfaces have molecules with chemical bonds that absorb and radiate electromagnetic energy in accord with their rotational, vibrational and electronic energy levels, which obey quantum mechanics and therefore occur at discrete wavelengths (see FIG. 4 for CO2 and H2O at lower temperatures). The two best examples relevant in fires are water and CO2 which emit in discrete bands. The soot (unburned carbonaceous particles) glows and provides most of the graybody radiation upon which the molecular radiation is superimposed. FIG. 4 shows that the higher the temperature, the more the curve of energy vs. wavelength approaches the shape of a blackbody emitter because emission from soot dominates the IR emission. At lower temperatures radiation from water, CO2, CO and other molecules dominates the emission and occurs at specific wavelengths.
Heat conduction occurs when there is a temperature gradient within a substance, regardless of whether it is a solid, liquid or gas. Calculating the temperature gradient in a solid as a function of time (i.e. transient heating) requires solving (Equation 5) which gives T(x,y,z,t) and in most cases numerical methods are used for complex geometries. For materials that are thin in the direction of heat conduction, simplifying assumptions can be made if the temperature gradient through the material (for example a foil) is negligible that reduce the transient heat conduction problem to algebra.
Equation 5. Heat equation for conduction in 3-dimensions:
            ∂      T              ∂      t        =                    (                  k                      ρ            ⁢                                                  ⁢            Cp                          )            ⁢                        ∇          2                ⁢        T              =                  (                  k                      ρ            ⁢                                                  ⁢            Cp                          )            ⁢              (                                                            ∂                2                            ⁢              T                                      ∂                              x                2                                              +                                                    ∂                2                            ⁢              T                                      ∂                              y                2                                              +                                                    ∂                2                            ⁢              T                                      ∂                              z                2                                                    )            
If the foil is thick, the heat equation (Equation 5) would need to be solved because the surface facing the IR radiation source would be significantly hotter than the back side where the thermocouple is attached. However, thin foils are easily analyzed using a so-called lumped capacitance thermal model (Incropera and Dewitt 1985). In this case, temperature gradients can be ignored when the Biot number is Bi<<1 (Equation 6). This situation is illustrated in FIG. 5.
Equation 6. Biot number:
  Bi  =                    h        rad            ⁢      L        k  
The Biot number is a dimensionless number that represents the ratio of heat transfer into the object (hradL) divided by the thermal conductivity of the material (k), where hrad is the heat transfer coefficient and L is the thickness. In the case of heating by convection, the heat transfer coefficient (hconv) for forced or free convection is used. For radiation, the concept of a heat transfer coefficient as a simple proportionality constant (as in Equation 1) has to be modified because the driving force for radiation depends on (Th4−Tc4) instead of ΔT. This problem can be circumvented by deriving an approximate heat transfer coefficient for radiation using the first term in a Taylor series expansion of σε(Th4−Tc4), which gives hrad=4σεTh3, where the source temperature (Th) is used. In the lumped capacitance model, the system is described by a time constant, which is given by Equation 7.
Equation 7. Thermal time constant for lumped capacitance model:
  τ  =            mC      p                      h        rad            ⁢      A      
Equation 8. Predicted temperature response for a free standing foil IR sensing element neglecting heat losses (T∞ is the temperature of the IR source and Ti is the starting temperature of the foil).
      T    ⁡          (      t      )        =                    (                              T            i                    -                      T            ∞                          )            ⁢              e                              -            t                    τ                      +          T      ∞      
Resistance temperature detectors (RTD) use a fine wire through which a constant current flows while the resistance is measured. The resistance of most metals increases with temperature (due to increased scattering of conduction electrons by lattice vibrations). The RTD can be calibrated to be extremely sensitive to small temperature changes. The fine wire is usually wrapped around a ceramic or glass core that is surrounded by a sheath to protect it from damage. One of the reasons that RTDs are popular in the process industries is that they are relatively immune to extraneous electrical noise and are stable. Common metals used in RTDs include Pt, Ni, Cu, and W.
Thermistors work by measuring the resistance of a semiconductor that has a constant current flow (similar to the RTD). Thermistors excel when precise measurements of low to moderate temperatures are required. In contrast to the RTD, as the temperature of a thermistor increases the resistance decreases because electrons from the valance band (or doping level) are thermally promoted into the conduction band, which increases the number of charge carriers, and reduces the electrical resistance. As with the RTD, the thermistor requires a very stable constant current source, and because semiconductors are used, these devices are usually limited to operating temperatures around 100° C.
IR thermometers use semiconductors such as PbS, Ge, Si, InAs, and InSb, which have narrow windows of wavelengths to which they respond. For example, the most sensitive detector (lead sulfide) detects radiation between 0.7 μm-3 μm. Indium antimonide (InSb) has a somewhat broader ranger (1-10 μm). Because all of the semiconductor based detectors have limited bandwidth responses and because these responses are highly nonlinear with wavelength (FIG. 7), semiconductor based IR detectors generally measure the intensity of radiation at one (or sometimes two) wavelengths and then fit the measured intensity to a graybody curve (which corresponds to a particular temperature) that has an assumed emissivity (which is selected on better instruments). The big advantage of semiconductor IR detectors is that they are very sensitive and when the emissivity of the emitter is known, can be very accurate (0.1-0.5%). The disadvantages are that they not mechanically robust, cannot tolerate high temperatures (like thermistors), require complex signal processing electronics and are relatively expensive.
Thermocouples are simple devices that rely on the difference in potentials (voltages) that exist in two different metals as a result of a temperature gradient. Metals are good electrical conductors because they have electrons that are more or less free to move through the crystal lattice under the influence of a potential. When a wire has temperatures that are different at each end, electrons will diffuse from the hot end to the cold end establishing an opposing internal potential that eventually stops the diffusion. The development of an internal potential in a metal that has a temperature gradient is called the Seebeck effect. In metals where the conduction electrons exhibit nearly “free-electron” behavior (Al, Mg, alkalis, etc.) electrons diffuse toward the cold end and such metals have negative Seebeck coefficients (FIG. 8). In other metals, the free electron picture does not really apply and it appears as if the electrons diffuse toward the hot end leading to positive Seebeck coefficients (Kasap 1997).
The sensitivity of this potential to temperature is termed the Seebeck coefficient (Equation 9). There is no way to measure this potential without completing a circuit, so in a thermocouple, a second wire with a different Seebeck coefficient is used for this purpose. The resulting voltage difference between the metals is given by (Equation 10)
Equation 9. Seebeck coefficient:
      S    Seebeck    =      dV    dT  
Equation 10. Thermocouple voltage resulting from the different Seebeck coefficients of two dissimilar metals:
      V    AB    =            ∫              T        o            T        ⁢                  (                              S            A                    -                      S            B                          )            ⁢      dT      
In most diagrams, a thermocouple is drawn as if it were attached to the test specimen with the wires joined together at a point because spot welding the wires together is the easiest way to make a thermocouple (FIG. 10 left). It should be pointed out however, that the junction has nothing to do with generating the voltage VAB; rather it is the difference in Seebeck coefficients of the two metals (Equation 10). Therefore, a thermocouple can be made where both wires are attached to another conductor and the temperature measurements will be accurate so long as the ends attached to the conductor are at the same temperature (FIG. 10 right). FIG. 9 shows specifications for various fine wire thermocouples and their thermal response times.
It is difficult to simultaneously measure the IR flux and ambient air temperature. Measuring the IR flux and ambient air temperature independently is more difficult than it first appears to be simply for the reasons that thermocouples, thermistors and RTDs are all heated by infrared radiation and heated or cooled by convection depending on the temperatures of the air and temperature sensing device.
The dirty environment or a fire causes problems on devices that rely on clean metal surfaces. For example, soot and ash can coat shiny metal surfaces (low emissivity materials), changing their emissivity.
Aspirated thermocouples can measure air temperatures in buildings during fire. In an aspirated TC, the TC is surrounded by a radiation shield and air is forced over the thermocouple at a high velocity. In effect, this increases the forced convection heat transfer to be large enough that convective controls the TC temperature. This approach suffers from the limitation that it is not suitable for applications where the firefighter has to wear the device because of the weight, complexity and mechanical unreliability of having to have a pump or heavy fan to generate air velocities upwards of 100 m/s.
SuperPASS™ 3 is a commercial-off-the-shelf sensor. PASS devices equipped with a temperature sensor exhibit very slow thermal responses (5-10 min) (FIG. 11 and FIG. 12).
These references contain at least one of the following limitations in regard to a portable burn warning device: inability to accurately measure (simultaneously) infrared radiation and convective heat, inability to work in the dirty fire environment, excessive weight, complexity, or mechanical unreliability.
There remains a need in the art for a fast responding temperature sensor that accurately responds to both infrared (IR) radiation and convective heating threats, that can be placed on or near the helmet (close to the SCBA face piece) to provide the firefighter with a warning before high temperatures can cause PPE failure.